State Estimation Research Articles

Output feedback control for non-strict feedback nonlinear systems: an adaptive fuzzy backstepping scheme

The adaptive fuzzy tracking control design issue is considered in this paper for a class of non-strict feedback nonlinear systems subject to external disturbances. A fuzzy high-gain state observer is constructed to reconstruct the unmeasurable states of the system by leveraging the universal approximation property of fuzzy logic systems for arbitrary unknown nonlinear functions. Within the framework of backstepping control design and in conjunction with adaptive techniques, an adaptive fuzzy control approach is presented. Subsequently, to work out the inherent ‘complexity explosion’ problem of the proposed control approach, dynamic surface control technique is introduced, leading to a simplified adaptive fuzzy output feedback control scheme. Stability analysis shows that the two proposed control schemes can ensure that all signals of the closed-loop system are semi-globally uniformly ultimately bounded, meanwhile the system tracking error can converge to a small neighborhood around the origin. Ultimately, a numerical simulation example is provided to validate the feasibility of the proposed control scheme.

Robust Nonlinear Model Predictive Control for the Trajectory Tracking of Skid-Steer Mobile Manipulators with Wheel–Ground Interactions

This paper presents a robust control strategy for trajectory-tracking control of Skid-Steer Mobile Manipulators (SSMMs) using a Robust Nonlinear Model Predictive Control (R-NMPC) approach that minimises trajectory-tracking errors while overcoming model uncertainties and terra-mechanical disturbances. The proposed strategy is aimed at counteracting the effects of disturbances caused by the slip phenomena through the wheel–terrain contact and bidirectional interactions propagated by mechanical coupling between the SSMM base and arm. These interactions are modelled using a coupled nonlinear dynamic framework that integrates bounded uncertainties for the mobile base and arm joints. The model is developed based on principles of full-body energy balance and link torques. Then, a centralized control architecture integrates a nominal NMPC (disturbance-free) and ancillary controller based on Active Disturbance-Rejection Control (ADRC) to strengthen control robustness, operating the full system dynamics as a single robotic body. While the NMPC strategy is responsible for the trajectory-tracking control task, the ADRC leverages an Extended State Observer (ESO) to quantify the impact of external disturbances. Then, the ADRC is devoted to compensating for external disturbances and uncertainties stemming from the model mismatch between the nominal representation and the actual system response. Simulation and field experiments conducted on an assembled Pioneer 3P-AT base and Katana 6M180 robotic arm under terrain constraints demonstrate the effectiveness of the proposed method. Compared to non-robust controllers, the R-NMPC approach significantly reduced trajectory-tracking errors by 79.5% for mobile bases and 42.3% for robot arms. These results highlight the potential to enhance robust performance and resource efficiency in complex navigation conditions.

Pitch control for floating offshore wind turbines via model-dependent extended state observer-based active disturbance rejection control

Various types of disturbances bring significant challenges to the stable operation of floating offshore wind turbines. This paper formulates the pitch control of floating offshore wind turbines using a novel model-dependent extended state observer-based active disturbance rejection control, which can effectively estimate and compensate for total disturbances. Firstly, a Markov model is proposed to describe wind and wave combined external disturbances and the aerodynamic characteristics of floating offshore wind turbines. Then, an active disturbance rejection control is developed based on the constructed model-dependent extended state observer. The approach provided in this paper can adjust the pitch angle to ensure that the generator speed output tracks the desired reference value. Based on this, the multi verse optimization algorithm is introduced to optimize the parameters of the controller. Finally, the superiorities of the results presented in this paper are illustrated by a 5 MW floating offshore wind turbine model. Simulation results demonstrate that the model-dependent extended state observer-based active disturbance rejection control strategy can significantly adjust the pitch angle to guarantee the stable operation of floating offshore wind turbines under wind and wave combined external disturbances.

Adaptive Time-Varying Formation Maneuvering Control for Multi-Robot Systems in Complex Obstacle-Rich Environments

To tackle the challenge of time-varying formation control for underactuated robots under model parameter uncertainties and environmental disturbances, this study proposes an affine formation control approach enhanced by an Extended State Observer. Initially, using affine positioning theory and polynomial interpolation, guidelines for selecting leader vehicles and trajectory planning methods are established, whereby the trajectory of follower vehicles is uniquely determined through the stress matrix. To address the cumulative disturbances arising from model uncertainties and environmental factors impacting the formation, an Extended State Observer with optimized parameters is introduced. Furthermore, a distributed affine formation control method with disturbance rejection is designed specifically for underactuated robots with “nonlinear, strongly coupled” dynamics, ensuring that the formation system can track the target configuration within bounded error margins. Finally, theoretical analysis and simulation outcomes ultimately confirm the efficacy of the control approach in achieving resilient formation tracking.

The Response of Tropopause-Overshooting Convection over North America to Climate Change

Abstract Recent field campaigns, observational studies, and modeling work have demonstrated that extratropical tropopause-overshooting convection has a substantial and previously underestimated impact on stratospheric water vapor concentrations. This necessitates improved understanding of how tropopause-overshooting convection will respond to a warming climate. A growing body of research indicates that environments conducive to severe thunderstorms will occur more often and be increasingly unstable in the future, but no study has examined how this may be related to increased overshooting. To rectify this, this study leverages an existing pseudo–global warming (PGW) experiment to evaluate potential future changes in tropopause-overshooting convection over North America. We examine two 10-yr simulations consisting of 1) a retrospective period (2003–12) forced by ERA-Interim initial and boundary conditions (the control simulation) and 2) the same retrospective period with CMIP5 ensemble-mean high-end emission scenario climate changes added to the initial and boundary conditions (the PGW simulation). Tropopause-overshooting convection in the control simulation is validated against observed overshoots from both ground-based radar observations in the United States and GOES observations over North America. The model is shown to effectively simulate the observed regional distribution, annual cycle, and diurnal cycle of tropopause-overshooting convection. In the PGW simulation, tropopause-overshooting convection is found to increase more than 250% across the model domain, and the projected seasonal period of frequent tropopause-overshooting convection is shown to extend into late summer. Additionally, tropopause-overshooting convection with extreme tropopause-relative heights (>4 km) is more frequent in a warmed climate scenario.

Discrete-time Luenberger observer design for Lithium-ion battery state-of-charge with stability guarantee

State-of-charge (SOC) estimation is particularly important as it provides information about the remaining energy capacity of the battery, allowing for better planning and utilization. Accurate SOC estimation is challenging because it cannot be directly measured from the battery. Instead, it is estimated by analyzing measurable variables such as current and voltage. To address this challenge, a discrete-time observer-based SOC estimation approach is proposed in this paper. This approach utilizes a second-order equivalent circuit model and a piecewise linear approximation to represent the relationship between SOC and open circuit voltage (OCV). The proposed observer-based approach utilizes these models to estimate the SOC with assured asymptotic stability under specific assumptions to simplify the design process. Simulations in Python are conducted to evaluate the performance of the designed observer. In the simulations, the SOC estimation under various conditions, such as model uncertainty, disturbances, and measurement noise, is also covered. In addition, three different observer gains are considered in the simulations. Lastly, simulation studies indicate that the estimated SOC values converge to the real SOC values, with some different behavior depending on the regarded situations.

Adaptive Robust Sensorless Control for PMSM Based on Improved Back EMF Observer and Extended State Observer

Adaptive Robust Sensorless Control for PMSM Based on Improved Back EMF Observer and Extended State Observer

Double-level prescribed performance control for rigid spacecraft attitude tracking under actuator faults

The problem of prescribed performance attitude tracking control for rigid spacecraft with external disturbance, inertia uncertainties and actuator faults on special orthogonal group SO(3) is investigated in this paper. With the aid of a novel Lyapunov function, a double-level prescribed performance controller is devised to ensure both attitude and angular velocity tracking errors converge within preset performance boundaries. By applying the suggested controller, the setting time, overshoot and steady-state error of both attitude and angular velocity tracking errors can be regulated by preset performance boundaries getting rid of the initial conditions of the control system. Distinguished from the exist prescribed performance controllers, a stricter performance boundary for angular velocity tracking error can be achieved. For the lumped disturbance which stems from the unknown external disturbance, inertia uncertainties and actuator faults, an extended state observer with linear feedback functions is initially designed to provide an estimation with simple structure. Rigorous proofs within a Lyapunov framework and comparison simulations are presented to demonstrate the effectiveness and superiority of the suggested control strategy.

Observer-based self-triggered adaptive decentralized control for uncertain interconnected nonlinear systems

In this paper, an observer-based self-triggered adaptive decentralized control method is presented for uncertain interconnected nonlinear systems (UINS) with unmeasured states. First, an adaptive state observer is constructed to estimate unmeasured system states. Then, the observer-based self-triggered controller is developed by applying the famous backstepping technique, in which the controller signal is updated based on the well-designed self-triggered protocol. Moreover, parameter adaptive laws are designed to address unknown parameters of UINS. Lyapunov theory is employed to prove that all signals of the UINS are semi-globally uniformly ultimately bounded (SGUUB) and the Zeno behavior will not appear. Simulation results manifest the efficacy of the derived self-triggered control solution.

A decoupling control of air supply for the PEM fuel cell with slide mode-active disturbance rejection controller

The air supply subsystem is crucial for optimizing proton exchange membrane fuel cells (PEMFCs). This study develops a transient model for the air subsystem and proposes a control strategy that decouples air pressure and flow using sliding mode-active disturbance rejection control (SM-ADRC). In this study, adjustments to the air compressor speed and the opening of the back-pressure valve are utilized to achieve this control strategy. The sliding mode-extended state observer (SM-ESO) is employed to estimate and compensate for uncertainties within the system, while the sliding mode-nonlinear state error feedback (SM-NLSEF) is used to simultaneously control air flow and pressure. The study evaluates the performance of the SM-ADRC controller across various scenarios and environmental pressures. Evaluations show that the SM-ADRC controller significantly outperforms traditional methods like Fuzzy-ADRC, ADRC, SMC, and PID, with overshoot reductions of 18.2%, 34.1%, 42.5%, and 63.7%, respectively, and adjustment time under 1 s. Additionally, SM-ADRC achieves a 4.1% and 1.8% improvement in efficiency compared to PID and ADRC.

On Active Disturbance Compression Control by Twice-Extended State Observer for Laser Pointing System

On Active Disturbance Compression Control by Twice-Extended State Observer for Laser Pointing System

Adaptive fuzzy optimal output-feedback fault-tolerant control for the USV system with intermittent actuator faults

This paper presents a novel fuzzy optimal output-feedback fault-tolerant control (FTC) method for uncertain nonlinear unmanned surface vehicle (USV) systems, which are subject to intermittent actuator failures and unmeasured states. The proposed optimal controller is composed of a fuzzy feedforward fault-tolerant output-feedback controller and a fuzzy error feedback optimal controller. The fuzzy feedforward fault-tolerant output-feedback controller is designed by using the fuzzy state observer and backstepping control design technique. The fuzzy optimal feedback controller is given by adopting adaptive dynamic programming (ADP) theory. It is proven that the presented fuzzy optimal FTC scheme is able to ensure that the USV system is uniformly ultimately bounded (UUB), and the optimal control performance is achieved. The validity is confirmed by computer simulation results.

Anti-Sway Adaptive Fast Terminal Sliding Mode Control Based on the Finite-Time State Observer for the Overhead Crane System

This work proposes an adaptive rapid terminal SMC (sliding mode control) approach based on the FFTSO (fast finite-time state observer) for overhead crane trajectory tracking and anti-swing control in the presence of external disturbances and parameter uncertainty. First, the system state observation under the constraint of unknown system parameters is accomplished by designing the FFTSO based on finite-time theory. Next, a parameter-adaptive fast terminal SMC is created for an overhead crane based on the model transformation. This technique can still monitor the intended trajectory and reduce payload swing even in cases when the payload mass and wire rope length are uncertain. Next, the Lyapunov theorem is used to demonstrate the stability of the overhead crane system’s positioning and anti-swing angle control mechanism. Lastly, the platform experiments confirm that the suggested closed-loop system control technique is successful.

Advanced sensorless control of a 12S/19P YASA-AFFSSPM motor using extended state observer and adaptive sliding mode control

This paper focuses on enhancing the sensorless control performance of a 12slots/19 poles yokeless and segmented armature axial flux-switching sandwiched permanent-magnet motor by proposing a rotor position Extended State Observer based on a extended back-EMF model method. Additionally, an adaptive sliding mode speed loop compensation method is introduced to address the significant cogging torque of the motor. By injecting the observed cogging torque as compensation into the q-axis current harmonic, this method aims to improve the motor's vibration and disturbance rejection performance in sliding mode control while eliminating steady-state errors in rotor speed and position estimation. The effectiveness of these control algorithms is validated through simulations and experiments under various operating conditions, demonstrating their potential for improving the position signal-free tracking performance of the investigated motor. The results indicate that the proposed control strategies achieve a maximum speed estimation error of approximately 1 rpm during steady-state operation and a maximum position estimation error of about 1.5°, showcasing high accuracy and robustness against disturbances.

PUSH AND PULL FACTORS AS DETERMINANTS OF FOREIGN DIRECT INVESTMENT: PANEL EVIDENCE FROM AFRICAN ECONOMIES

Foreign direct investment (FDI) plays a significant role in economic growth and development in African economies. While a range of factors affect FDI inflows, the examination of "push" and "pull" factors as key determinants has been sparse in the empirical literature. Hence, this study analyzed the "push" and "pull" impacts of foreign direct investment inflows in Africa spanning from 1996 to 2022. Thus, unlike previous studies, the current study employed static panel estimation methods to examine the determinants of FDI inflows in Africa. The findings of the fixed effect panel technique revealed that push factors have a negative and significant relationship with FDI inflows in Africa, suggesting that the poor performance of push factors in the recipient countries will discourage the inflows of FDI in Africa. Hence, recipient countries should adopt a push factors policy that would increase the inflows of foreign direct investment in African countries. Meanwhile, the pull factors do not determine FDI inflows in Africa during the period of investigation. Therefore, policymakers should adopt effective policy measures that make push factors responsive to attract more foreign investors.

Determinants of Energy Use in Turkish Manufacturing Industry: A Supply Side View

This paper aims to assess the supply-side determinants of firm-level energy use. To this end, we first propose a model for a stylized economy using Solovian framework, in which the production function employs energy input, along with capital and labor. We show the full algebraic solution of the model at the steady-state and in the transitional period and derive the supply-side determinants of energy consumption. Then, using firm-level micro panel data on the Turkish manufacturing industry from 2009 to 2015, we test the proposed model with static and dynamic panel data estimators. Our empirical results suggest that the proposed model is consistent with Turkish manufacturing data. Out of the supply-side determinants, firms’ output/value-added and total factor productivity, as a proxy for technological progress, are found to be the most significant determinants of firm-level energy use. Estimations also reveal quite heterogenous effects of technology on energy use in different manufacturing subsectors. Hence, although promoting technological change in the manufacturing industry is, without a doubt, the most convenient way to reduce energy use, policymakers should develop sector-specific incentives to achieve this goal.

An Extend Sliding Mode Disturbance Observer for Optical Inertial Platform Line-of–Sight Stabilized Control

As the imaging distance and focal length of photoelectric systems increase, the requirements for line-of–sight stabilization of optical inertial stabilized platforms (ISPs) become higher. Disturbance rejection directly determines the stability accuracy of optical inertial stabilized platforms. However, the accurate observation and suppression of wide-band and rapidly changing disturbances remains a challenge in current engineering applications. This paper proposes a robust extended sliding mode observer (ESMO) method to improve disturbance estimation performance. First, the linear extended state observer (LESO) is designed by taking the total disturbances as extended states. Then, a sliding mode observer (SMO) is incorporated in the extended states of the extended observer, forming a robust ESMO. Subsequently, the robustness and convergence characteristics of the proposed method are mathematically proved, revealing that it operates robustly without knowing the disturbance’s upper bound and offers faster dynamics and higher accuracy than the LESO. Finally, a series of simulation experimental tests are performed to demonstrate the effectiveness of the proposed method. The proposed method observes wide-band and rapidly changing disturbances utilizing the rapidly switching characteristic of the SMO and smooths the jitter of the SMO by cascading sliding mode estimation to the differentiation term of extended observation, achieving the integral effect of the reaching law. Meanwhile, this method only requires adjusting two parameters, making it suitable for engineering applications. It can be effectively used in optical inertial stabilized platform control systems for disturbance estimation and compensation.

Equilibrium Strategies in an Mn/M/1 Queue with Server Breakdowns and Delayed Repairs

Ophthalmic units use sophisticated equipment to enable accurate diagnosis of refractive errors. This equipment is subject to two types of breakdowns. One is simple breakdown which can be repaired in-house, and the other is complex breakdown which requires repair by the original equipment manufacturer (OEM) and results in a delay time between the server breakdown and the start of the repair. In this paper, we model this scenario as an Mn/M/1 queuing system with two types of breakdowns and delayed repairs due to complex breakdowns, where the delay time and repair times for simple and complex breakdowns are generally distributed. We obtain the steady-state probabilities and provide the recursive formulas for the Laplace–Stieltjes transforms (LSTs) of conditional residual delay time and repair times given the system state. For the fully observable case, we derive the equilibrium joining strategies of customers who decide to join or balk based on their observation of the system state. Moreover, two numerical experiments are conducted to explore the equilibrium joining probabilities.

Real-Time Temperature Field State Observer and Digital Replica to Support Cyber-Physical Testing

Real-Time Temperature Field State Observer and Digital Replica to Support Cyber-Physical Testing

The combined effects of retail energy prices, and exchange rates on inflation in Nigeria States

This paper explores the nonlinear dynamics relationship between petroleum product prices and inflation in Nigeria. By focusing on the role of exchange rate fluctuations in amplifying the relationships, the paper employs a multiplicative interaction approach to address the nonlinear effects of petroleum prices on inflation. Utilizing data from 2016: Q1 to 2024: Q2 from the National Bureau of Statistics and the Central Bank of Nigeria, the study introduces interaction terms to capture how petroleum prices and exchange rates interact to influence inflation. The methodology includes static and dynamic panel estimators, with a focus on the within effect model to account for unobserved state-specific factors. Key findings reveal that AGO and PMS prices significantly drive both headline and food inflation, while DPK's impact varies, and GAS shows minimal effect. The study highlights those geographical factors—proximity to seaports and fuel depots—significantly influence inflationary pressures. States closer to these facilities experience lower inflation due to reduced distribution costs. This suggests that policies aimed at partial subsidization for states farther from key infrastructure could mitigate regional inflation disparities. The findings contribute to the understanding of inflation dynamics, emphasizing the need for targeted policy interventions tailored to regional economic conditions in Nigeria.